Fundamental of MSD Module-III Part-a.ppt

Module - 3
Data Converter Fundamentals

Syllabus
 Ideal D/A Converter
 Ideal A/D Converter
 Quantization Noise
 Performance Limitations-
 Resolution
 Offset and Gain Error
 Accuracy and Linearity,
 Nyquist-rate D/A converters-
 Resistor String Converters
 Binary-Weighted Resistor Converters.

Data Converters:
Basic Concepts
 Analog signals are continuous, with infinite values in
a given range.
 Digital signals have discrete values such as on/off or
0/1.
 Limitations of analog signals
 Analog signals pick up noise as they are being amplified.
 Analog signals are difficult to store.
 Analog systems are more expensive in relation to digital
systems.

Data Converters: Basic Concepts
 Advantages of digital systems (signals)
 Noise can be reduced by converting analog signals in 0s
and 1s.
 Binary signals of 0s/1s can be easily stored in memory.
 Technology for fabricating digital systems has become so
advanced that they can be produced at low cost.
 The major limitation of a digital system is how
accurately it represents the analog signals after
conversion.

Embedded System
 A typical system that converts signals from analog to digital and back to
analog includes:
 A transducer that converts non-electrical signals into electrical signals
 An A/D converter that converts analog signals into digital signals
 A digital processor that processes digital data (signals)
 A D/A converter that converts digital signals into equivalent analog signals
 A transducer that converts electrical signals into real life non-electrical signals
(sound, pressure, and video)
So, how does A/D Converter works?

A/D Converter
 In order to change an analog signal
to digital, the input analog signal is
sampled at a high rate of speed.
 The amplitude at each of those
sampled moments is converted into a
number equivalent – this is called
quantization.
 These numbers are simply the
combinations of the 0s and 1s used
in computer language – this called
encoding.
http://www.cybercollege.com/tvp008.htm

A/D Conversion – Pulse Code
Modulation/Demodulation
PCM Signal
Modulation
Demodulation

Analog-to-Digital
 A simple hypothetical A/D converter circuit with one analog input signal and
three digital output lines with eight possible binary combinations: 000 to 111
 Shows the graph of digital output for FS V analog input
 The following points can be summarized in the above process:
 Maximum value this quantization process reaches is 7/8 V for a 1 V analog
signal; includes 1/8 V an inherent error
 1/8 V (an inherent error) is also equal to the value of the Least Significant Bit
(LSB) = 001.
 Resolution of a converter is defined in terms of the number of discrete values it
can produce; also expressed in the number of bits used for conversion or as 1/2n
where n =number of bits
 The value of the most significant bit (MSB) -100- is equal to ½ the voltage of the
full-scale value of 1 V.
 The value of the largest digital number 111 is equal to full-scale value minus the
value of the LSB.
 The quantization error can be reduced or the resolution can be improved by
increasing the number of bits used for the conversion
7/8

A little Detour: Opamp Review
 http://www.engin.brown.edu/courses/en123/L
ectures/DAconv.htm
 http://www.seas.upenn.edu/~ese206/labs/adc2
06/adc206.html

Opamps
 Ideal opamps
 Infinite BW
 Infinite voltage gain
 Infinite input impedance
 Zero output impedance
 Practical opamps
 wide BW
 Very high voltage gain
 Very high input impedance
 Very low output impedance
http://www.chem.uoa.gr/Applets/AppletOpAmps/Appl_OpAmps2.html

Closed Loop Frequency Response
 Non-inverting
 Source is connected to the non-
inverting input
 Feedback is connected to the
inverting input
 If Rf and Ri are zero, then unity
feedback used for buffering
 Av=1+Rf/Ri
 Inverting
 Feedback and source are
connected to the inverting input
 Av=-Rf/Ri

Comparators
 Determines which input is
larger
 A small difference
between inputs results
maximum output voltage
(high gain)
 Zero-level detection
 Non-zero-level detection
Max and minimum

Example
Vref = Vin(max).R2/(R1+R2)=1.63 V

A/D Conversion - Types
 Can be classified in four groups:
 Integrator:
 Charges a capacitor for a given amount of time using the analog signal.
 It discharges back to zero with a known voltage and the counter
provides the value of the unknown signal.
 Provides slow conversion but low noise.
 Often used in monitoring devices (e.g., voltmeters)
 Flash: uses multiple comparators in parallel.
 The known signal is connected to one side of the comparator and the
analog signal to be converted to the other side of the comparator.
 The output of the comparators provides the digital value.
 This is a high-speed, high cost converter.

A/D Conversion
 Flash Converter
 The circuit consists of 4 comparators
whose inverting inputs are connected to a
voltage divider.
 A comparator is basically an operational
amplifier used without feedback.
 The outputs of the comparators
correspond to a digital word.
 When the input rises above Vn1 , the first
comparator will switch to a high output
voltage causing the LED to light up,
indicating a (0001).
 For larger input voltages the output of
other comparators will switch high as
well. For large input voltages (above Vn3)
all comparators will be high
corresponding to (1111) digital output.

A/D Conversion
 Successive approximation: Includes a
D/A (digital to analog) converter and
a comparator. An internal analog
signal is generated by turning on
successive bits in the D/A converter.
 Counter: Similar to a successive
approximation converter except that
the internal analog signal is generated
by a counter starting at zero and
feeding it to the D/A converter.

Successive Approximation A/D
Converter Circuit
 The SAR (successive approximation
register) begins by turning on the MSB Bit7.
 Vo of the D/A converter is compared with the
analog input voltage Vin in the comparator.
 If analog voltage is less than the digital
voltage, Bit7 is turned off and Bit6 is turned
on.
 If analog voltage is greater than the digital
voltage, Bit7 is kept on and Bit6 is turned
on.
 The process of turning bit on/off is
continued until Bit0.
 Now the 8-bit input to the D/A
converter represents the digital
equivalent of the analog signal Vin.
Bit 7 is set: b7=1
If Va < Vd  b7=0; b6=1
If Va > Vd  b7=1; b6=1
…..
If Va < Vd  b7=0; …b0=1
If Va > Vd  b7=1; … b0=1
Done
Display

Sample and Hold
Circuit
 If the input voltage to an A/D converter is variable,
the digital output is likely to be unreliable and
unstable. Therefore, the varying voltage source is
connected to the ADC through a sample and hold
circuit.
 Basic Operation:
 When the switch is connected, it samples the input
voltage.
 When the switch is open, it holds the sampled voltage by charging the capacitor.
 Acquisition time: time to charge the capacitor after the switch is open and settle
the output.
 Conversion time: total time needed from the start of a conversion (turning on the
MSB in the SAR) until the end of the conversion (turning on/off Bit0 in the SAR)
- TAD: conversion time per bit.
ADG1211 Switch

A/D Examples
 Example 1
 Assumes the input analog voltage is changing between 0-5 V.
 Using a 3-bit A/D converter draw the output as the input signal ramps
from 0 to 5V.
 Calculate the resolution.
 What is the maximum possible voltage out? (this is called the full-
scale output)
 If the output is 1000 0000, what is the input?
 Example 2
 Assumes the input analog voltage is changing between -5 to 5 V;
using a 10-bit A/D converter.
 Calculate the number of quantization levels.
 Calculate the voltage resolution.

A/D Examples
 Example 1
 Assumes the input analog voltage is changing between 0-5 V.
 Using a 3-bit A/D converter draw the output as the input signal ramps
from 0 to 5V.
 Calculate the resolution. 1 / 2^8 = 19.53 mV
 What is the maximum possible voltage out? (this is called the full-
scale output) 5- Resolution
 If the output is 1000 0000, what is the input? MaxVolt / 2 = 2.5
 Example 2
 Assumes the input analog voltage is changing between -5 to 5 V;
using a 10-bit A/D converter.
 Calculate the number of quantization levels. 2^10
 Calculate the voltage resolution. 5-(-5)/1024=9.76 mV

PIC18F4520 Analog-to-Digital (A/D)
Converter Module (1 of 3)
 The PIC184520 microcontroller includes:
 10-bit A/D converter
 13 channels AN0 – AN12
 Three control registers
 ADCON0, ADCON1, and ADCON2

 ADCON0, ADCON1, and ADCON2
 ADRESH and ADRESL
VCFG1
VCFG0
ADRESH/L
16-bit
ADCON0

 Three control registers are used to:
 Set up the I/O pins for analog signals from
ports A, B, and E that are used as inputs for
A/D conversion. RA5
 Select a channel: AN4
 Set up pins RA2 and RA3 to connect
external VREF + and VREF - if specified in the
control register ADCON1.
 Select an oscillator frequency divider
through the control register ADCON2.
 Select an acquisition time through the control
register ADCON2.
If the input is 0-1V Vin=[0-1]:
Option1: Vref+ & Vref-  1V & GND
Option 2: Shift Vin to Vin’= Vin=[0-Vcc] and then Vref+ & Vref-  Vcc & GND

A/D Control Register0 (ADCON0)
 Primary function of the
ADCON0 register:
 Select a channel for input
analog signal
 Start a conversion
 Indicate the end of the
conversion
 Bit1 is set to start the
conversion, and at the
end of the conversion
this bit is reset.

A to D Control Register1
(ADCON1)
 ADCON1 is
primarily used to
set up the I/O pins
either for analog
signal or for
digital signals
(see Table 12.2)
and select VREF
voltages (see
Table 12.1).

A to D Control Register2 (ADCON2)
(1 of 2)
 Used to:
 Select an acquisition time and clock frequency
 Right or left justify output reading
 The output reading, after a conversion, is stored in
the 16-bit register ADRESH and ADRESL.
However, this is a 10-bit A/D converter leaving six
bit positions unused.
 Bit7 ADFM enables the user either to right justify or
left justify the 16-bit reading leaving the unused
positions as 0s.

A to D Control Register2
(ADCON2)
(2 of 2)

Example 12.3
 Interfacing a 10 k Pot

Example:
 What are the right questions?
 Where is the input connected to?
 Which channel is connected to the A/D
 Using external or internal clock
 What is the Vref?
 What is the minimum sampling time?
 What is the acquisition time?

Example
 Assumptions
 Use RA0 on the demo board.
 Use external oscillator
 Assuming conversion time (TAD) is 4 usec, what is the
clock frequency requirement (ADCON2)
 Assume acquisition time is 48 usec. What will be the
acquisition time setting?
 Write the program
 Set up the following registers properly:
 ADCON0, ADCON1, ADCON2.

Basic calculations:
Fosc = 4MHz
Tconv_time = TAD = 4usec =
1/(Fosc/x) x=16, hence, select
Fosc/16
Taqu-time = 48usec = y.
Tconv_time  y=12, hence select
12.TAD
Setting:
ADCON0 = 00 000 01
ADCON1 = 00 00 00 11
ADCON2 = 10 101 101
Example

Interfacing a Temperature Sensor
(1 of 7)
 Temperature sensor
 Transducer that converts temperature into an analog electrical signal
 Many are available as integrated circuits, and their outputs (voltage or
current) are, in general, linearly proportional to the temperature
 However, output voltage ranges of these transducers may not be
ideally suited to reference voltages of A/D converters
 Therefore, it is necessary to scale the output of a transducer to range
of the reference voltages of an A/D converter
 Scaling may require amplification or shifting of voltages at a different
level

(2 of 7)
 Temperature Sensor
 Interface the National Semiconductor LM34 temperature sensor to
channel 0 (AN0) of the A/D converter module as shown in Figure
12.11.
 Assume the output voltage of LM34 for the temperature range from
0ºF to 100ºF is properly scaled to 0 to +5 V.
 Write instructions to start a conversion, read the digital reading at the
end of the conversion, calculate the equivalent temperature reading in
degrees Fahrenheit, convert it into BCD, and store the reading in
ASCII code to the accuracy of one decimal point.
 The expected range of temperatures is 0ºF to 99.9ºF.

(3 of 7)
http://users.ipfw.edu/broberg/documents/LM34.pdf

(4 of 7)
 Hardware
 Temperature transducer LM34
 Three-terminal integrated circuit device that
can operate in the +5 V to +30 V power supply
range
 Outputs 10 mV/ºF linearly
 For the temperature range from 0ºF to
+99.9ºF; the output voltage range is 0 to 1 V
(rounded off to 100ºF).

(5 of 7)
 Scaling circuit
 To get the full dynamic range of the A/D conversion for
the output voltage range 0 to 1V of LM34:
 We can connect +VREF to +1 V or
 Scale the output voltage +1V to the voltage of the power supply
+5 V
 This scaling enables us to connect PIC18 power supply
VDD as voltage reference +VREF and ground Vss as –VREF.
0 V
1 V
0 V
5 V
Non-inverting opamp:
Av = 1 + Rf/Ri

Remember ….
Vref = Vin(max).R2/(R1+R2)=1.63 V

Non-Inverting Voltage Level Shifter
 Equations:
 A = (R4/R1) x (R1+R2)/(R3+R4)
 If R1= R3, and R2=R4, then A= (R4/R1)
 We want to convert a 10Vpp signal to a 3.3V signal so the gain should be 1/3. We can
choose R4 to be 33K and R1 to be 100K.
 We need to choose the positive offset such that the signal is centered at 1.6V.
 The gain off the offset voltage is:
 Aoffset= (R2+R1)/R1 x R3/(R3+R4) = R3/R1.
 For the previous resistor values, the gain is 1 since R3=R1, and so we use an offset voltage of
1.6V.

(6 of 7)
 Temperature calculations
 A/D converter has 10-bit resolution
 For temperature range 0ºF to +100ºF, the digital output
should be divided into 1023 steps (0 to 3FFH).
 Therefore, the digital value per degrees Fahrenheit is
10.23 (1023/100 = 10.2310).
 To obtain temperature reading from a digital reading of
the A/D converter, the digital reading must be divided by
the factor of 10.23.

(7 of 7)
 Software modules
 Program should be divided into the following:
 Setup all analog ports and channels
 Assume TAD = 12 and Fosc / 16
 Initialize A/D module (acquire analog input)
 Start a conversion and read the digital reading at the end of the
conversion.
 Multiply the temperature reading by 10
 Divide the 16-bit result by 102  QUO and REM  This is the
equivalent temperature reading.
 Convert the result in BCD.
 Convert the BCD numbers in ASCII code.

Digital to Analog (D/A, DAC, or
D-to-A) Conversion
 Converting discrete signals into discrete
analog values that represent the magnitude of
the input signal compared to a standard or
reference voltage
 The output of the DAC is discrete analog steps.
 By increasing the resolution (number of bits), the
step size is reduced, and the output approximates
a continuous analog signal.

Analysis of a Ladder Network
 A resistive ladder network is
a special type of series-
parallel circuit.
 One form of ladder network
is commonly used to scale
down voltages to certain
weighted values for digital-
to-analog conversion
 Called R/2R Ladder
Network
 To find total resistance of a
ladder network, start at the
point farthest from the source
and reduce the resistance in
steps.

The R/R2 Ladder Network
Only Input 4 is HIGH
Only Input 3 is HIGH
Used for Digital-to-analog converter!

Examining Digital-to-Analog Conversion
For Extra credit:
Change the circuit to generate this output:

Digital to Analog Conversion
 The resolution of a DAC is
defined in terms of bits—the
same way as in ADC.
 The values of LSB, MSB, and
full-scale voltages calculated the
same way as in the ADC.
 The largest input signal 111 is
equivalent of 7/8 of the full-scale
analog value.

D/A Converter Circuits (1 of 4)
 Can be designed using an operational amplifier and
appropriate combination of resistors
 Resistors connected to data bits are in binary
weighted proportion, and each is twice the value of
the previous one.
 Each input signal can be connected to the op amp by
turning on its switch to the reference voltage that
represents logic 1.
 If the switch is off, the input signal is logic 0.

D/A Converter Circuits (2 of 4)
 3-bit D/A Converter
Circuit
 R/2R Ladder Network for D/A Converter
Summing amplifier
The transfer function of the summing amplifier :
vo = -(v1/R1 + v2/R2 + … + vn/Rn)Rf
Thus if all input resistors are equal, the output is
a scaled sum of all inputs.
If they are different, the output is a weighted
linear sum of all inputs.

D/A Converter Circuits
 If the reference voltage is 1 V, and if all switches are
connected, the output current can be calculated as
follows:
 Output voltage
mA
0.875
8
1
4
1
2
1
k
1
V
R
V
R
V
R
V
I
I
I
I
I REF
3
REF
2
REF
1
REF
3
2
1
T
o 
















V
8
7
V
0.875
mA)
(0.875
k)
(1
I
R
V T
f
O 







Note that the output will be inverted!

D/A Converters as Integrated Circuits
 D/A converters are available
commercially as integrated circuits
 Can be classified in three categories.
 Current output, voltage output, and
multiplying type
 Current output DAC provides the current
IO as output signal
 Voltage output D/A converts IO into
voltage internally by using an op amp and
provides the voltage as output signal
 In multiplying DAC, the output is product
of the input voltage and the reference
source VREF.
 Conceptually, all three types are similar

Example 12.4
 What will be the analog equivalent of 1001 0001?
Vref = 5V

How can you generate a sine wave?
 Theoretically the voltages
would range from 0 to 5
 How do you change the
frequency? PIC

LAB
 Show that Example 12.3 on page 381 works.
 What is the range of the photoresistor
 Photoresistors (also often called phototransistors or
CdS photoconductive photocells)
 Simple resistors that altar resistance depending on the
amount of light place over them.
 Used in photovore is a robots (robots chasing light)
 Can also be used as color sensors how?
http://www.societyofrobots.com/sensors_color.shtml
You should find out the range of your
photoresistor as the light intensity
changes.

References
 http://www.engin.brown.edu/courses/en123/Lectures/DAconv.htm
 http://www.seas.upenn.edu/~ese206/labs/adc206/adc206.html
 Interesting project ideas: http://www.byonics.com/
 More interesting project ideas… http://www.ke4nyv.com/picprojects.htm

Generating a Ramp Waveform
Using a D/A Converter (1 of 3)
 Problem statement
 Write a subroutine to generate a ramp waveform
at the output of the D/A converter AD558 shown
in Figure 12–16. It is a voltage-output 8-bit DAC.
 The slope of the ramp should be variable based
on the delay count provided by the caller.

 Hardware
 The AD558 DAC requires ten signals from the
microcontroller: 8 bits for data input and two bits
for the control signals.
 8 bits of PORTC are connected as data input and the
two bits RE0 and RE1 of PORTE are used as control
signals.
 All bits should be initialized as outputs

 Software
 To generate a ramp: the Output should begin with zero and the
waveform should be increased incrementally.
 Can be done by setting a register as an up-counter starting from zero
and outputting that count.
 The output will begin with zero volts. As counter is incremented and
each count is outputted, the output waveform will increase in
magnitude in a straight line with a slope depending upon the delay
between counts.
 When counter reaches the maximum value FFH, it will be reset to 00
and start again. Therefore, the output will reach maximum value and
start again from zero, generating a ramp waveform.

Fundamental of MSD Module-III Part-a.ppt

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